STABLE SIZE DISTRIBUTION IN A MATHEMATICAL MODEL FOR TUMOR CELL POPULATION GROWTH DURING CHEMOTHERAPEUTICAL TREATMENT WITH TWO NON-CROSS RESISTANT DRUGS

1999 ◽  
Vol 07 (03) ◽  
pp. 285-306
Author(s):  
HAMILTON F. LECKAR ◽  
LAÉRCIO L. VENDITE
Keyword(s):  
Tumor Cell ◽  
Size Distribution ◽  
Genetic Mutation ◽  
Mixed Population ◽  
Linear Partial Differential Equations ◽  
Cell Population Growth ◽  
Chemotherapeutic Treatment ◽  
Stable Size Distribution ◽  
Distribution Theorem ◽  
Growth Of Tumor

A size-structured model is developed to study the growth of tumor cell populations during chemotherapeutic treatment with two non-cross resistant drugs, [Formula: see text] and [Formula: see text]. The cells reproduce by fission. Four types of cells are considered: sensitive cells to both [Formula: see text] and [Formula: see text], cells that are resistant to [Formula: see text] only, cells that are resistant to [Formula: see text] only, and cells that are resistant to both [Formula: see text] and [Formula: see text]. Resistant cells arise by spontaneous genetic mutation from sensitive cells and are selected during the growth of the mixed population. The model consists on a system of linear partial differential equations describing the size-density of each type of cells. That corresponds to chemotherapeutic treatment on a given time sequence intervals such that, we continuously apply [Formula: see text] at a first interval and next we apply [Formula: see text] at a second interval, and so forth. We obtain a stable size-distribution theorem for this case.

Abstract C239: BRAK/CXCL14 transgenic mice suppress growth of tumor cell xenografts

2009 ◽  
Author(s):  
Ryu‐Ichiro Hata ◽  
Kazuhito Izukur ◽  
Kenji Suzuki ◽  
Nobuyuki Yajima ◽  
Shin Ito ◽  
...  
Keyword(s):  
Transgenic Mice ◽  
Tumor Cell ◽  
Growth Of Tumor

scholarly journals A numerical study on the estimation of the stable size distribution for a cell population balance model

2018 ◽  
Vol 41 (8) ◽  
pp. 2894-2905 ◽  
Author(s):  
Luis M. Abia ◽  
Óscar Angulo ◽  
Juan Carlos López-Marcos ◽  
Miguel Ángel López-Marcos
Keyword(s):  
Size Distribution ◽  
Cell Population ◽  
Numerical Study ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
A Cell ◽  
Stable Size Distribution

Liposome mediated delivery of retinoids and aromatic polyamidines: Effects on growth of tumor cell lines

1991 ◽  
Vol 5 (S1) ◽  
pp. 23-24
Author(s):  
Claudio Nastruzzi ◽  
Giordana Feriotto ◽  
Peter Walde ◽  
Enea Menegatti ◽  
Roberto Gambari
Keyword(s):  
Tumor Cell ◽  
Cell Lines ◽  
Tumor Cell Lines ◽  
Growth Of Tumor

scholarly journals Stable Size Distribution of Amyloid Plaques Over the Course of Alzheimer Disease

2012 ◽  
Vol 71 (8) ◽  
pp. 694-701 ◽  
Author(s):  
Alberto Serrano-Pozo ◽  
Matthew L. Mielke ◽  
Alona Muzitansky ◽  
Teresa Gómez-Isla ◽  
John H. Growdon ◽  
...  
Keyword(s):  
Alzheimer Disease ◽  
Size Distribution ◽  
Amyloid Plaques ◽  
Stable Size Distribution

scholarly journals Growth of tumor emboli within a vessel model reveals dependence on the magnitude of mechanical constraint

2020 ◽  
Author(s):  
Jonathan Kulwatno ◽  
Jamie Gearhart ◽  
Xiangyu Gong ◽  
Nora Herzog ◽  
Matthew Getzin ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Tumor Cell ◽  
Cancer Progression ◽  
Tumor Burden ◽  
Cell Aggregates ◽  
Continuous Growth ◽  
The Matrix ◽  
Tumor Emboli ◽  
Growth Of Tumor ◽  
Mechanical Constraint

ABSTRACTTumor emboli – aggregates of tumor cell within vessels – pose a clinical challenge as they are associated with increased metastasis and tumor recurrence. When growing within a vessel, tumor emboli are subject to a unique mechanical constraint provided by the tubular geometry of the vessel. Current models of tumor emboli use unconstrained multicellular tumor spheroids, which neglect this mechanical interplay. Here, we modelled a lymphatic vessel as a 200 μm-diameter channel in either a stiff or soft, bioinert agarose matrix, and we modelled colon or breast cancer tumor emboli with aggregates of HCT116 or SUM149PT cells, respectively. The stiff vessel model constrained the tumor emboli to the cylindrical geometry, which led to continuous growth of the emboli, in contrast to the growth plateau that unconstrained spheroids exhibit. Emboli morphology in the soft vessel model, however, was dependent on the magnitude of mechanical mismatch between the vessel matrix and the cell aggregates. In general, when the elastic modulus of the vessel was greater than the emboli (Eves / Eemb > 1), the emboli were constrained to grow within the vessel geometry, and when the elastic modulus of the vessel was less than the emboli (0 < Eves / Eemb < 1), the emboli bulged into the matrix. Inhibitors of myosin-related force generation decreased the elastic modulus and/or increased the stress relaxation of the tumor cell aggregates, effectively increasing the mechanical mismatch. The increased mechanical mismatch after drug treatment was correlated with increased confinement of tumor emboli growth along the vessel, which may translate to increased tumor burden due to the increased tumor volume within the diffusion distance of nutrients and oxygen.INSIGHT BOXThe growth of tumor emboli—aggregates of tumor cells within vessels—is associated with aggressive cancer progression and metastasis. Models of their growth have not taken into account their biomechanical context, where radial expansion is constrained, but lengthwise expansion is free in the vessel. Here, we modelled the vessel geometry with a cylindrical microchannel in a hydrogel. In contrast to unconstrained or fully embedded aggregates, vessel-like constraint promotes growth of emboli in our model. The growth advantage is increased when the matrix is stiffened or actomyosin contractility weakened, both of which effectively increase the magnitude of mechanical constraint. This study sheds light on increased tumor burden in vessel-based growth and indicates a need to study tumor progression in similar environments.

scholarly journals Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control

2020 ◽  
Author(s):  
Jannatun Irana Ira ◽  
Md. Shahidul Islam ◽  
Jagadish Chandra Misra
Keyword(s):  
Optimal Control ◽  
Cell Growth ◽  
Tumor Growth ◽  
Mathematical Modelling ◽  
Tumor Cell ◽  
Tumor Cells ◽  
Treatment Process ◽  
Tumor Cell Growth ◽  
Growth Of Tumor ◽  
Over Time

The dynamics of tumor cell growth and its treatment process is discussed in this paper. We analyze some simple mathematical models and generalized models to understand the growth of tumor cells. A couple of diffusion models are discussed to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer and how cancer cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time.

scholarly journals Pan-Cancer Analysis of the Solute Carrier Family 39 Genes in Relation to Oncogenic, Immune Infiltrating, and Therapeutic Targets

2021 ◽  
Vol 12 ◽  
Author(s):  
Yi-Yuan Qu ◽  
Rong-Yan Guo ◽  
Meng-Ling Luo ◽  
Quan Zhou
Keyword(s):  
Tumor Cell ◽  
Cancer Progression ◽  
Therapeutic Targets ◽  
Genetic Mutation ◽  
Functional Enrichment ◽  
Solute Carrier Family ◽  
Clinical Prognosis ◽  
Immune Infiltration ◽  
Solute Carrier ◽  
Pan Cancer

Background: Emerging pieces of evidence demonstrated that the solute carrier family 39 (SLC39A) members are critical for the oncogenic and immune infiltrating targets in multiple types of tumors. However, the precise relationship between the SLC39A family genes and clinical prognosis as well as the pan-cancer tumor cell infiltration has not been fully elucidated.Methods: In this study, the pan-cancer expression profile, genetic mutation, prognostic effect, functional enrichment, immune infiltrating, and potential therapeutic targets of the SLC39A family members were investigated by analyzing multiple public databases such as the Oncomine, TIMER, GEPIA, cBioPortal, KM-plotter, PrognoScan, GeneMANIA, STRING, DAVID, TIMER 2.0, and CellMiner databases.Results: The expression levels of most SLC39 family genes in the tumor tissues were found to be significantly upregulated compared to the normal group. In mutation analysis, the mutation frequencies of SLC39A4 and SLC39A1 were found to be higher among all the members (6 and 4%, respectively). Moreover, the overall mutation frequency of the SLC39A family genes ranged from 0.8 to 6% pan-cancer. Also, the function of the SLC39A highly related genes was found to be enriched in functions such as zinc II ion transport across the membrane, steroid hormone biosynthesis, and chemical carcinogenesis. In immune infiltration analysis, the expression level of the SLC39A family genes was found to be notably related to the immune infiltration levels of six types of immune cells in specific types of tumors. In addition, the SLC39A family genes were significantly related to the sensitivity or resistance of 63 antitumor drugs in a variety of tumor cell lines.Conclusion: These results indicate that the SLC39 family genes are significant for determining cancer progression, immune infiltration, and drug sensitivity in multiple cancers. This study, therefore, provides novel insights into the pan-cancer potential targets of the SLC39 family genes.

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